(687f) Robust Economic Model Predictive Control with Zone Control

Nonlinear Model Predictive Control (NMPC) with general objective known as economic Model Predictive Control (EMPC) has received significant attention in recent years. The objective function of EMPC reflects some economic criterion such as profit maximization or heat minimization, etc which is different from traditional tracking NMPC where the objective is a positive definite quadratic function. The integration of process economics in the control layer makes EMPC of interest in many areas especially in the process industry [1].

Uncertainties arise as a result of imperfect models or unmeasured disturbances in a control system. The presence of disturbances in any control system can lead to performance degradation and/or loss of feasibility which can lead to loss of stability. Due to the integration of process economics in the control layer, it is not fully understood how the presence of uncertainties affect the operation of a system under EMPC. While several robust NMPC concepts has been introduced to address problems arising from the presence of uncertainties in stabilizing NMPC, simply transferring robust NMPC techniques to EMPC could result in poor economic performance [2]. This is because robust NMPC techniques have been designed to reject all disturbances to achieve its desired goal which may not be the case of EMPC as some disturbances can lead to better economic performance. To this end, some results on robust EMPC techniques have been proposed. However, they either use a min-max optimization approach or use the nominal model with tightened invariant constraints. In both cases, the computational demands are very high even for linear systems.

In this work, we present a novel economic Model Predictive Control formulation for controlling constrained nonlinear systems subject to unmeasured but bounded disturbances. The formulation incorporates the concept of economic risk in the controller design using only the nominal model and the zone control technique. This not only ensures that the closed-loop system and process economics are robust to disturbances, but also averts the computational demand encountered in the current approaches. This work extends the recent MPC formulation with zone tracking [3] to uncertain systems in a more general setting and can be considered as an economic trust region-based controller design. The key idea is to drive the states of the system to a robust positively invariant subset of the constrained space with specified economic performance. This is achieved by incorporating a fictitious zone tracking objective which is robust control invariant into the original economic objective. By creating a fictitious zone objective, the desired closed-loop economic performance in the presence of uncertainties can be specified in the controller design. We conduct rigorous stability analysis using input-to-state-stability and demonstrate the effectiveness of the proposed controller design using a CSTR example. An algorithm for the construction of the robust economic trust region is also presented.

References

[1] Ellis, M., Durand, H., & Christofides, P. D. (2014). A tutorial review of economic model predictive control methods. Journal of Process Control, 24(8), 1156-1178.

[2] Bayer, F. A., Müller, M. A., & Allgöwer, F. (2014). Tube-based robust economic model predictive control. Journal of Process Control, 24(8), 1237-1246.

[3] Liu, S., Mao, Y., & Liu, J. (2019). Model-Predictive Control with generalized zone tracking. IEEE Transactions on Automatic Control, 64(11), 4698-4704.